Constrained Nonlinear Regression

Notes

 | -------------------------------------------- | ------------------------------------------------ | 
 | Output Created                               | 21-MAY-2002 14:24:27                             | 
 | -------------------------------------------- | ------------------------------------------------ | 
 | Comments                                     |                                                  | 
 | ----------- | ------------------------------ | ------------------------------------------------ | 
 | Input       | Data                           | N:\YTO\TCDD\ABC kannat\SPSS\s242_abc_spss.sav    | 
 |             | ------------------------------ | ------------------------------------------------ | 
 |             | Filter                         | WLA                                              | 
 |             | ------------------------------ | ------------------------------------------------ | 
 |             | Weight                         | <none>                                           | 
 |             | ------------------------------ | ------------------------------------------------ | 
 |             | Split File                     | <none>                                           | 
 |             | ------------------------------ | ------------------------------------------------ | 
 |             | N of Rows in Working Data File | 70                                               | 
 | ----------- | ------------------------------ | ------------------------------------------------ | 
 | Syntax                                       | MODEL PROGRAM ED=1 EMIN=0 EMAX=3 N=1.            | 
 |                                              | COMPUTE PRED_ =                                  | 
 |                                              | emin+((emax-emin)*dose**n)/(ed**n+dose**n).      | 
 |                                              | CNLR toothdef                                    | 
 |                                              | /OUTFILE='C:\TEMP\spss193\SPSSFNLR.TMP'          | 
 |                                              | /PRED PRED_                                      | 
 |                                              | /BOUNDS ED <= 10000; ED >= 0.01; EMIN >= 0;      | 
 |                                              | N>=0; N<=5                                       | 
 |                                              | /CRITERIA STEPLIMIT 2 ISTEP 1E+20 .              | 
 |                                              |                                                  | 
 | ----------- | ------------------------------ | ------------------------------------------------ | 
 | Resources   | Elapsed Time                   | 0:00:00.11                                       | 
 | ----------- | ------------------------------ | ------------------------------------------------ | 


All the derivatives will be calculated numerically.




  Iteration Residual SS          ED        EMIN        EMAX           N

     0.3    104.0294400  1.00000000  .000000000  3.00000000  1.00000000
     1.1    59.50872316  1.33656370  .008285418  1.90326419  .986538180
     2.1    56.81949748  1.45727255  .296601307  1.89914257  .964062873
     3.2    51.93336734  4.60481966  .213897242  2.86017371  .455023975
     4.3    50.48720311  4.42237884  .161593065  2.81593040  .343757208
     5.3    48.08257166  3.54727758  .129544526  2.25946438  .541681541
     6.2    46.84292450  4.45988769  .008000134  2.55800263  .449490789
     7.1    46.56850429  4.82267776  .000000000  2.60504192  .420068314
     8.2    46.06554455  5.91969907  .000000000  2.67786843  .387829444
     9.1    45.33946497  7.79370785  .033743851  2.73091284  .399098922
    10.1    43.29694753  13.9761831  .274629863  2.75631822  .516843053
    11.1    41.95079533  20.5051152  .545965573  2.67288231  .684623132
    12.1    40.42117268  24.5426029  .539819643  2.62981835  .785594135
    13.1    38.93974477  32.8199047  .526840337  2.63578151  .971633277
    14.1    38.53420784  40.6697579  .600779361  2.63602395  1.15645476
    15.1    38.45643592  43.6714723  .555830687  2.68053832  1.21675443
    16.1    38.43143926  43.5883938  .577077893  2.66333006  1.22389206
    17.1    38.42626342  43.5740409  .579957227  2.65908288  1.23044012
    18.1    38.38590767  42.8885039  .594177931  2.62880076  1.28499817
    19.1    38.33296651  41.2170123  .602744934  2.59703626  1.35525838
    20.1    38.23835358  37.2575862  .604863892  2.55381231  1.48742772
    21.1    38.16723421  34.5831461  .594638324  2.54433734  1.60571361
    22.1    38.14057574  34.5947745  .584604159  2.55856344  1.68561171
    23.1    38.13927396  34.2221244  .583747202  2.55523676  1.71561859
    24.1    38.13884911  34.1360136  .584545393  2.55241051  1.73841843
    25.1    38.13880551  34.1109198  .585245630  2.55114302  1.74520627
    26.1    38.13880470  34.1174703  .585372604  2.55110397  1.74538031
    27.1    38.13880468  34.1180211  .585387424  2.55111109  1.74528248

Run stopped after 27 major iterations.
Optimal solution found.





Nonlinear Regression Summary Statistics     Dependent Variable TOOTHDEF

  Source                 DF  Sum of Squares  Mean Square

  Regression              4      169.36120       42.34030
  Residual               66       38.13880         .57786
  Uncorrected Total      70      207.50000

  (Corrected Total)      69       89.20000

  R squared = 1 - Residual SS / Corrected SS =     .57243

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  ED        34.118021079 12.771721766  8.618455832 59.617586326
  EMIN        .585387424   .131596018   .322647498   .848127351
  EMAX       2.551111093   .202758476  2.146290734  2.955931451
  N          1.745282483  1.035002891  -.321167462  3.811732428

  Asymptotic Correlation Matrix of the Parameter Estimates

                  ED      EMIN      EMAX         N

  ED          1.0000     .2416     .4637    -.1967
  EMIN         .2416    1.0000    -.0996     .3076
  EMAX         .4637    -.0996    1.0000    -.4751
  N           -.1967     .3076    -.4751    1.0000

Constrained Nonlinear Regression

Notes

 | -------------------------------------------- | ------------------------------------------------ | 
 | Output Created                               | 21-MAY-2002 14:24:27                             | 
 | -------------------------------------------- | ------------------------------------------------ | 
 | Comments                                     |                                                  | 
 | ----------- | ------------------------------ | ------------------------------------------------ | 
 | Input       | Data                           | N:\YTO\TCDD\ABC kannat\SPSS\s242_abc_spss.sav    | 
 |             | ------------------------------ | ------------------------------------------------ | 
 |             | Filter                         | WLB                                              | 
 |             | ------------------------------ | ------------------------------------------------ | 
 |             | Weight                         | <none>                                           | 
 |             | ------------------------------ | ------------------------------------------------ | 
 |             | Split File                     | <none>                                           | 
 |             | ------------------------------ | ------------------------------------------------ | 
 |             | N of Rows in Working Data File | 63                                               | 
 | ----------- | ------------------------------ | ------------------------------------------------ | 
 | Syntax                                       | MODEL PROGRAM ED=1 N=1 EMIN=0 EMAX=3 .           | 
 |                                              | COMPUTE PRED_ =                                  | 
 |                                              | emin+((emax-emin)*dose**n)/(ed**n+dose**n).      | 
 |                                              | CNLR toothdef                                    | 
 |                                              | /OUTFILE='C:\TEMP\spss193\SPSSFNLR.TMP'          | 
 |                                              | /PRED PRED_                                      | 
 |                                              | /BOUNDS ED <= 10000; ED >= 0.01; EMIN >= 0;      | 
 |                                              | N>=0; N<=5                                       | 
 |                                              | /CRITERIA STEPLIMIT 2 ISTEP 1E+20 .              | 
 |                                              |                                                  | 
 | ----------- | ------------------------------ | ------------------------------------------------ | 
 | Resources   | Elapsed Time                   | 0:00:00.09                                       | 
 | ----------- | ------------------------------ | ------------------------------------------------ | 


All the derivatives will be calculated numerically.




  Iteration Residual SS          ED           N        EMIN        EMAX

     0.2    134.3180793  1.00000000  1.00000000  .000000000  3.00000000
     1.1    60.33150664  1.58756073  .984076790  .000000000  1.46359997
     2.2    58.66607906  4.34985422  .511367563  .000000000  2.53041178
     3.1    58.33198114  4.43850102  .632973640  .000000000  2.51364218
     4.1    53.27108117  3.45719026  .764018474  .000000000  1.95259094
     5.1    52.37593403  3.91915714  .781949861  .000000000  1.96854175
     6.2    48.27318689  7.07984923  .929015556  .000000000  2.07836536
     7.1    48.07881731  7.52960238  .998077676  .067252602  2.05161621
     8.1    43.69174467  13.6382795  1.38003666  .150583592  2.17640661
     9.1    39.27492981  23.2627680  1.99745554  .191785448  2.31483175
    10.1    37.74854444  30.9909733  2.51892606  .189182140  2.36926073
    11.1    37.64275148  33.4087411  2.71458611  .209549868  2.35424249
    12.1    37.63785845  33.5771713  2.72259922  .187731161  2.35796697
    13.1    37.63039788  33.4627206  2.72477058  .195981461  2.35499270
    14.1    37.62235952  33.3563517  2.73702643  .201186708  2.35293290
    15.1    37.59340879  32.9793453  2.80045725  .212724977  2.34661097
    16.1    37.54388600  32.3826412  2.93999618  .223030702  2.33798304
    17.1    37.46041354  31.6271286  3.22550135  .227978240  2.32814638
    18.1    37.35269707  31.3198273  3.67029012  .222214528  2.32407748
    19.1    37.26827406  31.4309449  4.21367295  .207361304  2.32610374
    20.2    37.24058836  30.9281074  4.68500370  .194519771  2.32340823
    21.1    37.23074386  31.3026237  5.00000000  .194468232  2.32713994
    22.1    37.22797465  31.1136631  5.00000000  .196312955  2.32567409
    23.1    37.22764793  31.0858483  5.00000000  .198401051  2.32530092
    24.1    37.22763204  31.0932404  5.00000000  .198973619  2.32529251
    25.1    37.22763186  31.0951721  5.00000000  .199010895  2.32530710

Run stopped after 25 major iterations.
Optimal solution found.


Nonlinear Regression Summary Statistics     Dependent Variable TOOTHDEF

  Source                 DF  Sum of Squares  Mean Square

  Regression              4      101.52237       25.38059
  Residual               59       37.22763         .63098
  Uncorrected Total      63      138.75000

  (Corrected Total)      62       91.60317

  R squared = 1 - Residual SS / Corrected SS =     .59360




                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  ED        31.095172141  8.863541309 13.359266947 48.831077334
  N          5.000000000 34.288287215 -63.61070424 73.610704240
  EMIN        .199010895   .132311961  -.065744728   .463766518
  EMAX       2.325307101   .213200294  1.898694299  2.751919904

  Asymptotic Correlation Matrix of the Parameter Estimates

                  ED         N      EMIN      EMAX

  ED          1.0000    -.8892    -.1864     .4847
  N           -.8892    1.0000     .3098    -.4227
  EMIN        -.1864     .3098    1.0000    -.1297
  EMAX         .4847    -.4227    -.1297    1.0000

Constrained Nonlinear Regression

Notes

 | -------------------------------------------- | ------------------------------------------------ | 
 | Output Created                               | 21-MAY-2002 14:24:27                             | 
 | -------------------------------------------- | ------------------------------------------------ | 
 | Comments                                     |                                                  | 
 | ----------- | ------------------------------ | ------------------------------------------------ | 
 | Input       | Data                           | N:\YTO\TCDD\ABC kannat\SPSS\s242_abc_spss.sav    | 
 |             | ------------------------------ | ------------------------------------------------ | 
 |             | Filter                         | WLC                                              | 
 |             | ------------------------------ | ------------------------------------------------ | 
 |             | Weight                         | <none>                                           | 
 |             | ------------------------------ | ------------------------------------------------ | 
 |             | Split File                     | <none>                                           | 
 |             | ------------------------------ | ------------------------------------------------ | 
 |             | N of Rows in Working Data File | 54                                               | 
 | ----------- | ------------------------------ | ------------------------------------------------ | 
 | Syntax                                       | MODEL PROGRAM ED=1 N=1 EMIN=0 EMAX=3 .           | 
 |                                              | COMPUTE PRED_ =                                  | 
 |                                              | emin+((emax-emin)*dose**n)/(ed**n+dose**n).      | 
 |                                              | CNLR toothdef                                    | 
 |                                              | /OUTFILE='C:\TEMP\spss193\SPSSFNLR.TMP'          | 
 |                                              | /PRED PRED_                                      | 
 |                                              | /BOUNDS ED <= 10000; ED >= 0.01; EMIN >= 0;      | 
 |                                              | N>=0; N<=5                                       | 
 |                                              | /CRITERIA STEPLIMIT 2 ISTEP 1E+20 .              | 
 |                                              |                                                  | 
 | ----------- | ------------------------------ | ------------------------------------------------ | 
 | Resources   | Elapsed Time                   | 0:00:00.09                                       | 
 | ----------- | ------------------------------ | ------------------------------------------------ | 


All the derivatives will be calculated numerically.




  Iteration Residual SS          ED           N        EMIN        EMAX

     0.2    54.76289954  1.00000000  1.00000000  .000000000  3.00000000
     1.2    34.00851718  1.59496632  .973815908  .000000000  1.91425542
     2.3    32.29411234  1.71531684  .953280196  .204044517  1.91995384
     3.2    28.63212099  3.00734861  .768813138  .159464239  2.59689939
     4.1    27.56694125  3.76403071  1.48692297  .429947900  2.51261052
     5.1    26.71138768  4.25838769  1.91853333  .499394007  2.38323279
     6.1    25.97067624  5.02850737  2.14013321  .337632695  2.38493717
     7.1    25.61194548  5.40848040  2.26277627  .417121449  2.40739890
     8.1    25.34435757  5.95810735  2.30421910  .456779155  2.45156608
     9.1    24.74331350  7.50928313  2.25887490  .511384356  2.56888880
    10.1    24.32884417  8.95490371  2.13292761  .517154089  2.64822487
    11.1    24.12386239  9.55023183  1.94974456  .486780511  2.65823623
    12.1    24.06043905  9.77367987  1.71903702  .462596446  2.67027822
    13.1    24.05170802  9.80047151  1.61853995  .457696507  2.68796642
    14.1    24.04909101  9.77152751  1.60386760  .458909520  2.69900086
    15.1    24.04891200  9.74476252  1.60588661  .459219471  2.70043153
    16.1    24.04889805  9.73334834  1.60520301  .459014125  2.70002736
    17.1    24.04889379  9.72383990  1.60563891  .458869432  2.69931192
    18.1    24.04889377  9.72381756  1.60564073  .458872874  2.69927201

Run stopped after 18 major iterations.
Optimal solution found.


Nonlinear Regression Summary Statistics     Dependent Variable TOOTHDEF

  Source                 DF  Sum of Squares  Mean Square

  Regression              4      101.70111       25.42528
  Residual               50       24.04889         .48098
  Uncorrected Total      54      125.75000

  (Corrected Total)      53       62.37500

  R squared = 1 - Residual SS / Corrected SS =     .61445

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  ED         9.723817563  3.714477033  2.263070870 17.184564255
  N          1.605640728   .874471835  -.150787644  3.362069100
  EMIN        .458872874   .136235808   .185235200   .732510548
  EMAX       2.699272010   .349130573  1.998022617  3.400521404




  Asymptotic Correlation Matrix of the Parameter Estimates

                  ED         N      EMIN      EMAX

  ED          1.0000    -.3385     .1646     .6677
  N           -.3385    1.0000     .3949    -.6595
  EMIN         .1646     .3949    1.0000    -.1897
  EMAX         .6677    -.6595    -.1897    1.0000

